Vertex and Edge Connectivity of the Zero Divisor graph \(\Gamma[\mathbb{Z}_n]\)

Abstract

The Zero divisor Graph \(\Gamma[R]\) of a commutative ring \(R\) is a graph with vertex set being the set of non-zero zero divisors of \(R\) and there is an edge between two vertices if their product is zero. In this paper, we prove that the vertex, edge connectivity and the minimum degree of the zero divisor graph \(\Gamma[\mathbb{Z}_n]\) for any natural number \(n\), are equal.